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Regle Yüzeylere Farklı Yaklaşımlar

Year 2012, Volume: 7 Issue: 1, 56 - 68, 04.06.2012

Abstract

Özet: Bu çalışmada, yüzeyler dual vektörler ve doğru transformasyonları kullanılarak tanımlanmaktadır. Sonrasında parametrik yüzey transformasyonları için yeni bir yaklaşım verilmektedir. Üç boyutlu geometric öğeler için temeli dual birim vektörlere dayanan temsili dual eğri ve dual yüzey modeli ileri sürülmektedir. Burada bazı bilinen yeni yaklaşımlar kullanılmaktadır. Ayrıca, Bishop ve Frenet geometrik tanımları sunulmaktadır. Sonuç olarak, Blaschke ve Darboux yaklaşımları arasındaki analitik mukayese ve ilişki, metodumuzun doğruluğu gösterilerek belirtilmektedir.

References

  • Bottema O., Roth B., 1979. Theoretical kinematics, North-Holland Publishing Company, New York, p. 558.
  • Gugenheimer H.W., 1956. Differential Geometry, McGraw-Hill, New York, pp. 162-169.
  • Hacısalihoglu H.H., 1983. Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi, Fen- Edebiyat Fakültesi Yayınları, p. 338.
  • Hacısalihoglu H.H., 1972. On the pitch of a closed ruled surface, Mech. Mach. Theory 7: 291-305
  • Hacısalihoglu H.H., 1972. On the pitch of a closed ruled surface, Mech. Mach. Theory 7: 291-305
  • Liu H., Wang F., 2008. Mannheim partner curves in 3-space, Journal of Geometry, 88: 120-126.
  • Papageorgiou S.G., Aspragathos N., 2006. Transformation and Normal Vector Calculation of Parametrically Defined Surfaces Based on Dual Vectors and Screw Theory: Application to Phong's Shading Model, Computer Graphics Forum, 25: 183-195.
  • Phillip A., Nikos A., 2001. Computer graphics representation and transformation of geometric entities using dual unit vectors and line transformations, Computers & Graphics, 25: 195-209.
  • Monterde J., Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion, preprint submitted to Elsevier Science.
  • Özkaldı S., İlarslan K., Yaylı Y., 2009. On Mannheim Partner Curve in Dual Space, Analele Stiintifice
  • ale Universitatii Ovidius Constanta, 17 (2): 131-142.
  • Rashad A.A.B., 2005. One-Parameter Closed Dual Spherical Motions and Holditch's Theorem Sitzungsber, Abt. II, 214: 27-41.
  • Rashad A.A.B., 2003. On the Blaschke Approach of Ruled Surface, Tamkang Journal of Math, 34 (2): 107-116.
  • Shifrin T., 2010. Differential Geometry: A first Course in Curves and Surfaces, University of Georgia, p.125.
  • Yaylı Y., 2000. On the Motion of the Frenet Vectors and Spacelike Ruled Surfaces in the Minkowski 3-Space, Mathematical and Computational Applications, 5 (1): 49-55.
  • Yaylı Y., Saracoglu S., 2012. Ruled Surfaces and Dual Spherical Curves, Acta Universitatis Apulensis,No. 30 (accepted)
  • Yaylı Y., Saracoglu S., 2010. Different Approaches to to Ruled Surfaces, XVI. Geometrical Seminar, 20-25 September, Serbia. (presented)
  • Clifford W.K., 1873. On the Hypotheses which Underlie the Foundations of Geometery, Proc. London Math. Soc., 4: 381.
  • Yusuf Yaylı e-mail: yayli@science.ankara.edu.tr

Different Approaches To Ruled Surfaces

Year 2012, Volume: 7 Issue: 1, 56 - 68, 04.06.2012

Abstract

Abstract: In this study, surfaces are defined by using dual vectors and
line transformations. A new approach is given for the transformation of
parametrically surfaces. Dual curve and dual surface representational
model for 3-dimensional geometric entities based on dual unit vectors
are proposed. Some well-known new approaches like Blaschke approach of
ruled surfaces are used. Moreover, geometric explanations of Bishop and
Frenet are presented. Finally, an analytical comparison and the relation
between Blaschke and Darboux approaches are represented showing the
merits of our method.

References

  • Bottema O., Roth B., 1979. Theoretical kinematics, North-Holland Publishing Company, New York, p. 558.
  • Gugenheimer H.W., 1956. Differential Geometry, McGraw-Hill, New York, pp. 162-169.
  • Hacısalihoglu H.H., 1983. Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi, Fen- Edebiyat Fakültesi Yayınları, p. 338.
  • Hacısalihoglu H.H., 1972. On the pitch of a closed ruled surface, Mech. Mach. Theory 7: 291-305
  • Hacısalihoglu H.H., 1972. On the pitch of a closed ruled surface, Mech. Mach. Theory 7: 291-305
  • Liu H., Wang F., 2008. Mannheim partner curves in 3-space, Journal of Geometry, 88: 120-126.
  • Papageorgiou S.G., Aspragathos N., 2006. Transformation and Normal Vector Calculation of Parametrically Defined Surfaces Based on Dual Vectors and Screw Theory: Application to Phong's Shading Model, Computer Graphics Forum, 25: 183-195.
  • Phillip A., Nikos A., 2001. Computer graphics representation and transformation of geometric entities using dual unit vectors and line transformations, Computers & Graphics, 25: 195-209.
  • Monterde J., Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion, preprint submitted to Elsevier Science.
  • Özkaldı S., İlarslan K., Yaylı Y., 2009. On Mannheim Partner Curve in Dual Space, Analele Stiintifice
  • ale Universitatii Ovidius Constanta, 17 (2): 131-142.
  • Rashad A.A.B., 2005. One-Parameter Closed Dual Spherical Motions and Holditch's Theorem Sitzungsber, Abt. II, 214: 27-41.
  • Rashad A.A.B., 2003. On the Blaschke Approach of Ruled Surface, Tamkang Journal of Math, 34 (2): 107-116.
  • Shifrin T., 2010. Differential Geometry: A first Course in Curves and Surfaces, University of Georgia, p.125.
  • Yaylı Y., 2000. On the Motion of the Frenet Vectors and Spacelike Ruled Surfaces in the Minkowski 3-Space, Mathematical and Computational Applications, 5 (1): 49-55.
  • Yaylı Y., Saracoglu S., 2012. Ruled Surfaces and Dual Spherical Curves, Acta Universitatis Apulensis,No. 30 (accepted)
  • Yaylı Y., Saracoglu S., 2010. Different Approaches to to Ruled Surfaces, XVI. Geometrical Seminar, 20-25 September, Serbia. (presented)
  • Clifford W.K., 1873. On the Hypotheses which Underlie the Foundations of Geometery, Proc. London Math. Soc., 4: 381.
  • Yusuf Yaylı e-mail: yayli@science.ankara.edu.tr
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Makaleler
Authors

Yusuf Yaylı

Semra Saraçoğlu This is me

Publication Date June 4, 2012
Published in Issue Year 2012 Volume: 7 Issue: 1

Cite

IEEE Y. Yaylı and S. Saraçoğlu, “Different Approaches To Ruled Surfaces”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 7, no. 1, pp. 56–68, 2012.